Journal of Scientific Computing
Element-by-Element Post-Processing of Discontinuous Galerkin Methods for Timoshenko Beams
Journal of Scientific Computing
Journal of Scientific Computing
Journal of Scientific Computing
Boundary-Conforming Discontinuous Galerkin Methods via Extensions from Subdomains
Journal of Scientific Computing
Optimal Convergence of the Original DG Method on Special Meshes for Variable Transport Velocity
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Discontinuous Galerkin Methods for Delay Differential Equations of Pantograph Type
SIAM Journal on Numerical Analysis
Computational aspects of the new discontinuous Galerkin method
F-and-B'11 Proceedings of the 4th WSEAS international conference on Finite differences - finite elements - finite volumes - boundary elements
An $hp$-Version Discontinuous Galerkin Method for Integro-Differential Equations of Parabolic Type
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
High order splitting schemes with complex timesteps and their application in mathematical finance
Journal of Computational and Applied Mathematics
hp-adaptive IPDG/TDG-FEM for parabolic obstacle problems
Computers & Mathematics with Applications
Journal of Scientific Computing
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The discontinuous Galerkin finite element method (DGFEM) for the time discretization of parabolic problems is analyzed in the context of the hp-version of the Galerkin method. Error bounds which are explicit in the time steps as well as in the approximation orders are derived and it is shown that the hp-DGFEM gives spectral convergence in problems with smooth time dependence. In conjunction with geometric time partitions it is proved that the hp-DGFEM results in exponential rates of convergence for piecewise analytic solutions exhibiting singularities induced by incompatible initial data or piecewise analytic forcing terms. For the h-version DGFEM algebraically graded time partitions are determined that give the optimal algebraic convergence rates. A fully discrete hp scheme is discussed exemplarily for the heat equation. The use of certain mesh-design principles for the spatial discretizations yields exponential rates of convergence in time and space. Numerical examples confirm the theoretical results.